A majorization-minimization approach to design of power distribution networks
Abstract
We consider optimization approaches to design cost-effective electrical networks for power distribution. This involves a trade-off between minimizing the power loss due to resistive heating of the lines and minimizing the construction cost (modeled by a linear cost in the number of lines plus a linear cost on the conductance of each line). We begin with a convex optimization method based on the paper 'Minimizing Effective Resistance of a Graph' [Ghosh, Boyd & Saberi]. However, this does not address the Alternating Current (AC) realm and the combinatorial aspect of adding/removing lines of the network. Hence, we consider a non-convex continuation method that imposes a concave cost of the conductance of each line thereby favoring sparser solutions. By varying a parameter of this penalty we extrapolate from the convex problem (with non-sparse solutions) to the combinatorial problem (with sparse solutions). This is used as a heuristic to find good solutions (local minima) of the non-convex problem. To perform the necessary non-convex optimization steps, we use the majorization-minimization algorithm that performs a sequence of convex optimizations obtained by iteratively linearizing the concave part of the objective. A number of examples are presented which suggest that the overall method is a good heuristicmore »
- Authors:
-
- Los Alamos National Laboratory
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1000948
- Report Number(s):
- LA-UR-10-02039; LA-UR-10-2039
TRN: US201101%%727
- DOE Contract Number:
- AC52-06NA25396
- Resource Type:
- Conference
- Resource Relation:
- Conference: 49th IEEE Conference on Decision and Control ; December 15, 2010 ; Atlanta, GA
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 24 POWER TRANSMISSION AND DISTRIBUTION; ALGORITHMS; ALTERNATING CURRENT; CONSTRUCTION; DESIGN; HEATING; OPTIMIZATION; POWER DISTRIBUTION
Citation Formats
Johnson, Jason K, and Chertkov, Michael. A majorization-minimization approach to design of power distribution networks. United States: N. p., 2010.
Web.
Johnson, Jason K, & Chertkov, Michael. A majorization-minimization approach to design of power distribution networks. United States.
Johnson, Jason K, and Chertkov, Michael. 2010.
"A majorization-minimization approach to design of power distribution networks". United States. https://www.osti.gov/servlets/purl/1000948.
@article{osti_1000948,
title = {A majorization-minimization approach to design of power distribution networks},
author = {Johnson, Jason K and Chertkov, Michael},
abstractNote = {We consider optimization approaches to design cost-effective electrical networks for power distribution. This involves a trade-off between minimizing the power loss due to resistive heating of the lines and minimizing the construction cost (modeled by a linear cost in the number of lines plus a linear cost on the conductance of each line). We begin with a convex optimization method based on the paper 'Minimizing Effective Resistance of a Graph' [Ghosh, Boyd & Saberi]. However, this does not address the Alternating Current (AC) realm and the combinatorial aspect of adding/removing lines of the network. Hence, we consider a non-convex continuation method that imposes a concave cost of the conductance of each line thereby favoring sparser solutions. By varying a parameter of this penalty we extrapolate from the convex problem (with non-sparse solutions) to the combinatorial problem (with sparse solutions). This is used as a heuristic to find good solutions (local minima) of the non-convex problem. To perform the necessary non-convex optimization steps, we use the majorization-minimization algorithm that performs a sequence of convex optimizations obtained by iteratively linearizing the concave part of the objective. A number of examples are presented which suggest that the overall method is a good heuristic for network design. We also consider how to obtain sparse networks that are still robust against failures of lines and/or generators.},
doi = {},
url = {https://www.osti.gov/biblio/1000948},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri Jan 01 00:00:00 EST 2010},
month = {Fri Jan 01 00:00:00 EST 2010}
}